What is the ruling on reciting the first Tashahhud in the last rakaʿah of supererogatory prayers without sending blessings upon the Prophet?

Praying upon the Prophet (peace be upon him) in the final Tashahhud is, according to the preponderant opinion, one of the pillars of prayer. Therefore, whoever intentionally omits it, their prayer is invalid and must be repeated if it was an obligatory prayer. As for whoever omits it out of forgetfulness and does not remember until after finishing the prayer, and the interval was not long, they must perform it and what comes after it and prostrate for forgetfulness. If the interval was long, the prayer is invalidated.